It takes a lot of propellant to perform any significant maneuver in space. You'd then have to spend about the same amount of energy to undo the results of that maneuver. The trajectory to fly to the moon and enter the right orbit is pretty tight. The vehicle flying to the moon would have a hard time dodging an incoming missile because the amount of acceleration is pretty low in most cases and the vehicle has a lot of momentum. Even turning the spacecraft 90 degrees off course and firing the thruster at full blast wouldn't result in a very large course change before you'd have to stop and get back on course. It's a far cry from the violent evasive maneuvers fighter pilots pull to get away from a missile. Sad to say it, but Hollywood always gets that wrong.

Since a missile would be far less massive than the target and isn't worried about hitting a narrow window, it's freer to maneuver. A modified version of the kinetic kill vehicle on the NMD missiles could do the job. It could be launched on an intercept trajectory then make more extensive course corrections than the target is capable of making. In fact, it might be easier to hit this kind of target than an ICBM RV.

Of course, a directed energy weapon would be easier but that would probably require putting a lot more infrastructure on the moon, an expensive process.